Abstract
We consider the dynamics of a logistic neutral delay system which is continuous in time and discrete in space. Such a system models the growth of a single-species population distributed over a ring of identical patches and it allows for population dispersing from one patch to its nearest neighbors. We shall show that (i) in the case of instantaneous dispersion feedback, the dispersal in the local growth rate and the neutral term have a stablizing effect on the population dynamics; (ii) increasing the delay in the growth phase changes the stability of a positive equilibrium and leads to a Hopf bifurcation of synchronous or phase-locked oscillations if the dispersion is small; (iii) the neutral term may bring about several global branches of phase-locked oscillations which would not occur in the absence of a neutral term, .and hence the neutral term in this situation has a destablizing influence.
